Question: Simplify the following expression: $ x = \dfrac{1}{9} - \dfrac{-7a}{a - 1} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{a - 1}{a - 1}$ $ \dfrac{1}{9} \times \dfrac{a - 1}{a - 1} = \dfrac{a - 1}{9a - 9} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{-7a}{a - 1} \times \dfrac{9}{9} = \dfrac{-63a}{9a - 9} $ Therefore $ x = \dfrac{a - 1}{9a - 9} - \dfrac{-63a}{9a - 9} $ Now the expressions have the same denominator we can simply subtract the numerators: $x = \dfrac{a - 1 + 63a }{9a - 9} $ Distribute the negative sign: $x = \dfrac{a - 1 + 63a}{9a - 9}$ $x = \dfrac{64a - 1}{9a - 9}$